For the tensor perturbation \(h_{ij}\)  to the metric, we use the transverse and traceless conditions (REF ). To be specific, we express the components of \(h_{ij}\)  to be \(h_{ij}=h_+ e_{ij}^{+}+h_{\times } e_{ij}^{\times }\) , where \(e_{ij}^{+}\)  and \(e_{ij}^{\times }\)  obey the relations
of \(e_{ij}^{+}(k)e_{ij}^{+}(-k)^{\ast }=1\) , \(e_{ij}^{\times }(k)e_{ij}^{\times }(-k)^{\ast }=1\) , and \( e_{ij}^{+}(k)e_{ij}^{\times }(-k)^{\ast }=0\)  in the Fourier space with \(k\)  being the comoving wave number. To obtain the tensor perturbation equations for our model, we first expand the action (REF ) up to the second order  [1]}, [2]}, [3]},
\(S^{(2)}_T=\sum _{\lambda =+,\times }\int dt \, d^{3}x \, M_{pl}^{2}\frac{a^3}{8}\Big [\dot{h}_{\lambda }^2-\frac{1}{a^2}(\partial h_{\lambda }^2)\Big ].\) 
